Enriques surfaces and Leech lattice

Abstract: Let $L$ be an even unimodular lattice of signature $(1,25)$ which is unique up to isomorphisms. J.H. Conway found a fundamental domain $C$ of the reflection group of $L$ by using a theory of Leech lattice. Recently S. Brandhorst and I. Shimada have classified all primitive embeddings of $E_{10}(2)$ into $L$, where $E_{10}(2)$ is the pullback of the Picard lattice of an Enriques surface to the covering K3 surface. There are exactly $17$ embeddings. By restricting $C$ to the positive cone of $E_{10}\otimes {\bf R}$ we obtain $17$ polyhedrons. In this talk I would like to discuss the automorphism groups of Enriques and Coble surfaces in terms of these polyhedrons.

algebraic geometrynumber theory

Audience: researchers in the topic

“Algebraic geometry and arithmetic” Viacheslav Nikulin’s 70th birthday conference

Series comments: The conference is dedicated to the 70th birthday of our colleague and friend Viacheslav Nikulin, who made a huge contribution to the theory of K3 surfaces and also other domains of geometry and arithmetic, including reflection groups, automorphic forms and infinite-dimensional Lie algebras. Topics of the conference reflect mathematical interests of the hero of the day.